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This work appears to be based on the older Surya Siddhanta and uses the midnight-day reckoning, as opposed to sunrise in Aryabhatiya. A third text, which may have survived in the Arabic translation, is Al ntf or Al-nanf. It claims that it is a translation by Aryabhata, but the Sanskrit name of this work is not known. Direct details of Aryabhata's work are known only from the Aryabhatiya.

The name "Aryabhatiya" is due to later commentators. Aryabhata himself may not have given it a name. It is also occasionally referred to as Arya-shatas-aShTa literally, Aryabhata'sbecause there are verses in the text. Thus, the explication of meaning is due to commentators. The Aryabhatiya presented a number of innovations in mathematics and astronomy in verse form, which were influential for many centuries.

The extreme brevity of the text was elaborated in commentaries by his disciple Bhaskara I Bhashyac. Aryabhatiya is also well-known for his description of relativity of motion. He expressed this relativity thus: "Just as a man in a boat moving forward sees the stationary objects on the shore as moving backward, just so are the stationary stars seen by the people on earth as moving exactly towards the west.

The place-value system, first seen in the 3rd-century Bakhshali Manuscriptwas clearly in place in his work. While he did not use a symbol for zerothe French mathematician Georges Ifrah argues that knowledge of zero was implicit in Aryabhata's place-value system as a place holder for the powers of ten with null coefficients. However, Aryabhata did not use the Brahmi numerals.

Continuing the Sanskritic tradition from Vedic timeshe used letters of the alphabet to denote numbers, expressing quantities, such as the table of sines in a mnemonic form. By this rule the circumference of a circle with a diameter of 20, can be approached. After Aryabhatiya was translated into Arabic c. Aryabhata discussed the concept of sine in his work by the name of ardha-jyawhich literally means "half-chord".

For simplicity, people started calling it jya. When Arabic writers translated his works from Sanskrit into Arabic, they referred it as jiba.

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However, in Arabic writings, vowels are omitted, and it was abbreviated as jb. Later writers substituted it with jaibmeaning "pocket" or "fold in a garment ". In Arabic, jiba is a meaningless word. Later in the 12th century, when Gherardo of Cremona translated these writings from Arabic into Latin, he replaced the Arabic jaib with its Latin counterpart, sinuswhich means "cove" or "bay"; thence comes the English word sine.

This problem was also studied in ancient Chinese mathematics, and its solution is usually referred to as the Chinese remainder theorem. It turns out that the smallest value for N is In general, diophantine equations, such as this, can be notoriously difficult. In AryabhatiyaAryabhata provided elegant results for the summation of series of squares and cubes: [ 27 ].

Aryabhata's system of astronomy was called the audAyaka systemin which days are reckoned from udaydawn at lanka or "equator". Some of his later writings on astronomy, which apparently proposed a second model or ardha-rAtrikAmidnight are lost but can be partly reconstructed from the discussion in Brahmagupta 's Khandakhadyaka. In some texts, he seems to ascribe the apparent motions of the heavens to the Earth's rotation.

He may have believed that the planet's orbits are elliptical rather than circular.

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Aryabhata correctly insisted that the Earth rotates about its axis daily, and that the apparent movement of the stars is a relative motion caused by the rotation of the Earth, contrary to the then-prevailing view, that the sky rotated. In the same way that someone in a boat going forward sees an unmoving [object] going backward, so [someone] on the equator sees the unmoving stars going uniformly westward.

The cause of rising and setting [is that] the sphere of the stars together with the planets [apparently? Aryabhata described a geocentric model of the Solar System, in which the Sun and Moon are each carried by epicycles. They in turn revolve around the Earth. The positions and periods of the planets was calculated relative to uniformly moving points.

In the case of Mercury and Venus, they move around the Earth at the same mean speed as the Sun. In the case of Mars, Jupiter, and Saturn, they move around the Earth at specific speeds, representing each planet's motion through the zodiac. Most historians of astronomy consider that this two-epicycle model reflects elements of pre-Ptolemaic Greek astronomy.

Solar and lunar eclipses were scientifically explained by Aryabhata. He states that the Moon and planets shine by reflected sunlight. Instead of the prevailing cosmogony in which eclipses were caused by Rahu and Ketu identified as the pseudo-planetary lunar nodeshe explains eclipses in terms of shadows cast by and falling on Earth.

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Thus, the lunar eclipse occurs when the Moon enters into the Earth's shadow verse gola. He discusses at length the size and extent of the Earth's shadow verses gola. Later Indian astronomers improved on the calculations, but Aryabhata's methods provided the core. His computational paradigm was so accurate that 18th-century scientist Guillaume Le Gentilduring a visit to Pondicherry, India, found the Indian computations of the duration of the lunar eclipse of 30 August to be short by 41 seconds, whereas his charts by Tobias Mayer, were long by 68 seconds.

Considered in modern English units of time, Aryabhata calculated the sidereal rotation the rotation of the earth referencing the fixed stars as 23 hours, 56 minutes, and 4. Similarly, his value for the length of the sidereal year at days, 6 hours, 12 minutes, and 30 seconds As mentioned, Aryabhata advocated an astronomical model in which the Earth turns on its own axis.

Thus, it has been suggested that Aryabhata's calculations were based on an underlying heliocentric model, in which the planets orbit the Sun, [ 38 ] [ 39 ] [ 40 ] though this has been rebutted.

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Brahmi numerals Hindu—Arabic numeral system Symbol for zero 0 Infinite series expansions for the trigonometric functions. Rangacarya — P. Sengupta — B. Datta — T. Hayashi A. Krishnaswamy Ayyangar — A. Singh — C. Rajagopal — T. Saraswati Amma — S. Sen — K. Shukla — K. Sarma — Babylon China Greece Islamic mathematics Europe. While studying at the university, Aryabhata produced the Aryabhatiyahis major work.

Written at the age of just 23, it ranges widely across mathematics and astronomy, but is particularly notable for its calculations regarding planetary periods. Aryabhata also worked out a value for pi that equates to 3. Using this value, he was able to calculate that the Earth had a circumference of 24, miles. This is correct to within 0.

A Aryabhata crater 25 F. Aryabhata satellite 5 F. Aryabhatta college 9 F. Pages in category "Aryabhata" This category contains only the following page. A Creator:Aryabhata. Media in category "Aryabhata" The following 24 files are in this category, out of 24 total. Aryabhatiya of Aryabhata, English translation.